A298259 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 5 or 8 king-move adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 3, 3, 0, 0, 2, 1, 2, 0, 0, 11, 4, 4, 11, 0, 0, 13, 3, 11, 3, 13, 0, 0, 34, 7, 23, 23, 7, 34, 0, 0, 65, 14, 72, 86, 72, 14, 65, 0, 0, 123, 35, 201, 238, 238, 201, 35, 123, 0, 0, 266, 89, 597, 604, 895, 604, 597, 89, 266, 0, 0, 499, 242, 1705, 2492, 3335, 3335, 2492

Offset: 1

Author

R. H. Hardin, Jan 15 2018

Keywords

• nonn
• tabl

Comments

Table starts

.0...0..0....0....0.....0......0.......0........0.........0.........0

.0...1..3....2...11....13.....34......65......123.......266.......499

.0...3..1....4....3.....7.....14......35.......89.......242.......643

.0...2..4...11...23....72....201.....597.....1705......5141.....15305

.0..11..3...23...86...238....604....2492.....7722.....26880.....93816

.0..13..7...72..238...895...3335...13980....55889....230402....953813

.0..34.14..201..604..3335..13991...70095...331341...1644480...8037526

.0..65.35..597.2492.13980..70095..435534..2412035..14299708..83146969

.0.123.89.1705.7722.55889.331341.2412035.16014301.112395697.777907073

Examples

			Some solutions for n=7 k=4
..0..0..1..1. .0..0..1..1. .0..0..0..0. .0..0..1..1. .0..0..1..1
..0..1..0..1. .0..1..0..1. .0..1..1..0. .0..1..0..1. .0..1..0..1
..1..0..1..0. .0..1..1..0. .1..0..1..0. .0..1..1..0. .0..1..1..0
..1..1..0..0. .0..0..0..0. .1..0..0..0. .0..1..0..1. .0..1..0..1
..1..0..1..0. .1..1..1..1. .0..1..1..0. .0..0..0..1. .0..1..0..1
..0..1..1..0. .1..1..1..1. .1..0..0..1. .0..1..1..0. .1..0..0..1
..0..0..0..0. .1..1..1..1. .1..1..1..1. .1..1..0..0. .1..1..1..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..220

Crossrefs

Column 2 is A297870.

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

k=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4)

k=3: [order 18] for n>19

k=4: [order 53] for n>54